In this paper, another type of derivation in B-algebra is defined, by defining two self-maps, one... more In this paper, another type of derivation in B-algebra is defined, by defining two self-maps, one of which is a derivation in B-algebra (denoted by d) and the other is called generalization of derivation in B-algebra (denoted by D). Based on this definition, some properties of generalized -derivation and generalized -derivation in B-algebra are constructed, then there is one common property, that is if d and D are identity functions, then D is regular. Then, the concept is used as a reference to define the generalized -derivation in B-algebra. In the last section, we discuss some properties of generalized -derivations in B-algebras.
Pada artikel ini didefinisikan konsep generalisasi left-right t-derivasi ((l, r)-t-derivasi) dan ... more Pada artikel ini didefinisikan konsep generalisasi left-right t-derivasi ((l, r)-t-derivasi) dan generalisasi right-left t-derivasi ((r, l)-t-derivasi) di B-aljabar dan diselidiki sifat-sifatnya. Kemudian, juga diselidiki sifat-sifat dari suatu generalisasi t-derivasi yang regular di B-aljabar. Pada bagian akhir, dibahas sifat-sifat generalisasi (l, r)-t-derivasi dan generalisasi (r, l)-t-derivasi di B-aljabar 0-komutatif.
A BN-algebra is a non-empty set X with a binary operation “∗” and a constant 0 that satisfies the... more A BN-algebra is a non-empty set X with a binary operation “∗” and a constant 0 that satisfies the following axioms: (B1) x∗x=0, (B2) x∗0=x, and (BN) (x∗y)∗z=(0∗z)∗(y∗x) for all x, y, z ∈X. A non-empty subset I of X is called an ideal in BN-algebra X if it satisfies 0∈X and if y∈I and x∗y∈I, then x∈I for all x,y∈X. In this paper, we define several new ideal types in BN-algebras, namely, r-ideal, k-ideal, and m-k-ideal. Furthermore, some of their properties are constructed. Then, the relationships between ideals in BN-algebra with r-ideal, k-ideal, and m-k-ideal properties are investigated. Finally, the concept of r-ideal homomorphisms is discussed in BN-algebra.
In this paper, we introduce the definition of ideal in B-algebra and some relate properties. Also... more In this paper, we introduce the definition of ideal in B-algebra and some relate properties. Also, we introduce the definition of prime ideal in B-algebra and we obtain some of its properties.
In this paper, we introduce the definition of ideal in B-algebra and some relate properties. Also... more In this paper, we introduce the definition of ideal in B-algebra and some relate properties. Also, we introduce the definition of prime ideal in B-algebra and we obtain some of its properties.
In this paper, another type of derivation in B-algebra is defined, by defining two self-maps, one... more In this paper, another type of derivation in B-algebra is defined, by defining two self-maps, one of which is a derivation in B-algebra (denoted by d) and the other is called generalization of derivation in B-algebra (denoted by D). Based on this definition, some properties of generalized -derivation and generalized -derivation in B-algebra are constructed, then there is one common property, that is if d and D are identity functions, then D is regular. Then, the concept is used as a reference to define the generalized -derivation in B-algebra. In the last section, we discuss some properties of generalized -derivations in B-algebras.
Pada artikel ini didefinisikan konsep generalisasi left-right t-derivasi ((l, r)-t-derivasi) dan ... more Pada artikel ini didefinisikan konsep generalisasi left-right t-derivasi ((l, r)-t-derivasi) dan generalisasi right-left t-derivasi ((r, l)-t-derivasi) di B-aljabar dan diselidiki sifat-sifatnya. Kemudian, juga diselidiki sifat-sifat dari suatu generalisasi t-derivasi yang regular di B-aljabar. Pada bagian akhir, dibahas sifat-sifat generalisasi (l, r)-t-derivasi dan generalisasi (r, l)-t-derivasi di B-aljabar 0-komutatif.
A BN-algebra is a non-empty set X with a binary operation “∗” and a constant 0 that satisfies the... more A BN-algebra is a non-empty set X with a binary operation “∗” and a constant 0 that satisfies the following axioms: (B1) x∗x=0, (B2) x∗0=x, and (BN) (x∗y)∗z=(0∗z)∗(y∗x) for all x, y, z ∈X. A non-empty subset I of X is called an ideal in BN-algebra X if it satisfies 0∈X and if y∈I and x∗y∈I, then x∈I for all x,y∈X. In this paper, we define several new ideal types in BN-algebras, namely, r-ideal, k-ideal, and m-k-ideal. Furthermore, some of their properties are constructed. Then, the relationships between ideals in BN-algebra with r-ideal, k-ideal, and m-k-ideal properties are investigated. Finally, the concept of r-ideal homomorphisms is discussed in BN-algebra.
In this paper, we introduce the definition of ideal in B-algebra and some relate properties. Also... more In this paper, we introduce the definition of ideal in B-algebra and some relate properties. Also, we introduce the definition of prime ideal in B-algebra and we obtain some of its properties.
In this paper, we introduce the definition of ideal in B-algebra and some relate properties. Also... more In this paper, we introduce the definition of ideal in B-algebra and some relate properties. Also, we introduce the definition of prime ideal in B-algebra and we obtain some of its properties.
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